Question

check whether - 150 is a term of the AP 11,8,5,2

Answer 1

Mahlaan

Let -150 be an Ap

by using formula

-150=11+(n-1)(-3)
by solving
n=139/3 +1
n = 142/3
Here n is not an natural no. therefore -150 is not an term of Ap.

Answer 2

a=11
d=8-11=-3

Let -150 be the nth term of AP.

$nth \: term \: = - 150 \\ a + (n - 1)d = - 150 \\ 11 + (n - 1)( - 3) = - 150 \\ (n - 1)( - 3) = - 150 - 11 \\ (n - 1)( - 3) = - 161 \\ (n - 1) = \frac{ - 161}{ - 3} \\ n - 1 = 53.66 \\ n = 54.66 \\ \\ the \: term \: of \: ap \: cannot \: be \: in \: decimal$
So -150 is not the term of AP